SOLUTION: Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
4 sec2 x − 4 sec
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Question 919648: Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
4 sec2 x − 4 sec x = 8
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
4 sec2 x − 4 sec x = 8
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Divide thru by 4 to get:
sec^2(x) - sec(x)- 2 = 0
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Factor::
(sec(x)-2)(sec(x)+1) = 0
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sec(x) = 2 or sec(x) = -1
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x = arccos(1/2) = 60 degrees or - 60 degrees
x = arccos(-1) = 180 degrees
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Cheers,
Stan H.
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